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A binary powering Schur algorithm for computing primary matrix roots. (English) Zbl 1202.65053

The authors propose a new algorithm based on the Schur normal form, for computing a primary \(p\)th root of an \(n \times n\) complex matrix. They prove that the cost of the proposed algorithm is lowered to \({\mathcal{O}}(n^2 p + n^3 \log_2 p)\) ops and the storage is lowered to \({\mathcal{O}}(n p + n^2 \log_2 p)\) real numbers.

MSC:

65F30 Other matrix algorithms (MSC2010)
15A24 Matrix equations and identities
15A16 Matrix exponential and similar functions of matrices

Software:

mftoolbox; mctoolbox
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References:

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